trying to understand
so the CLT is only applicable for data sets where ‘if you could get a large enough sample’ you’d see that the distribution is normal?
The key is to differentiate between the distribution of the sample (which we assume in some way approximates the distribution of the population, so if the population is not normal, neither should this distribution be) and the sampling distribution, which is the distribution of the averages of many samples. If I select a sample of 100, I can draw a graph of value vs. frequency, with the frequencies summing to 100, since I have 100 items in my sample. The shape of that should approximate the shape of a graph drawn for a sample of 10M, which is the entire population. I haven’t added any normality by doing that.
On the other hand, I can draw a sample of 100, and find the average value. Then I can repeat this process 100 times, and graph the value of the average against how often that average was obtained. This one will be more normal than the first graph (if the requirements of CLT are met.) If I increase not the number of samples, but the sample size (draw 200 instead of 100), then it will be more normal.
When is this true? When we have a trait which can be fairly observed by drawing a simple random sample, when the trait is random and independent (can’t be predicted by some other trait), and when the mean and sd of the population are finite.
so i imagine rothbard has a problem with all the statisticians assuming these things when they set about their economic analysis. if they do asume these things. if they dont asume these things , are they therefore using methods other than CLT?
What statisticians do is they first verify these conditions - the first 3 conditions can be reasoned out and have to do with experiment design, the last 2 can be calculated to check that they are finite.
Correct me if I’m wrong but could you not just criticize the potential abuse of statistics by saying that the majority of economic variables which are worth drawing inference from are not of an independent nature. If for example we want to analyze various prices it would seem that they are fundamentally dependent nature, that is, they are interelated through a complex web of relations. A price in one area is intricately related to price in another area and therefore there height is not independent in nature. I suppose if they’re random to a sufficient degree it can be overlooked, but the most interesting aspect of complex systems is the relations of its elements. These relations determine the values of the elements. I guess if you could reduce the relations to random underlying causes, you could go on? I don’t know. I suppose I’m probably way off. I’ve taken many econometrics course but I never pay attention (it’s really boring).
No, I tend to think that this is true. There are many good criticisms of the use of statistics: ordinal preference, subjectivity, time, the fact that so much of mainstream economics simply misuses them anyway (there’s a good audio from the Keynes conference at Mises.org about this in relation to the Phillips curve), human action, … I think what you’ve pointed out here is true also. If there’s enough randomness, you can factor out the dependence, but only by using a stratified random sample. Yes, you could also reduce the relations, but in economics, there is no random underlying factor (except maybe human action).
human action is by definition not random, its purposeful, and this is why im skeptical that for the prupose of studying economics:
Human action is purposeful from the perspective of the actor. From the perspective of an observer, a particular action seems random, though, since we don’t have access to their plans and purposes. I don’t mean seems random in the sense of “oh, that seems like a random thing to do” but rather that we cannot predict ahead of time what a person will do. If I walk into an auction house, I understand what’s happening there, but without getting into everyone’s brains, I can’t predict who will buy what, or for how much. I can make some guesses “John really likes those kinds of things, I bet he’ll bid on it” but it doesn’t take me very far. I agree entirely, though, that this whole thing is not amenable to the theory of statistics and probability.
The big problem that I’ve encountered with economic statistical analysis is the not the size or distribution of the data or sampling errors, it’s understanding what you’re really measuring.
For instance, say I have a database full of price information. If you work from the understanding that all prices are relative, then they are in fact relative only to those prices at that particular instance when they were measured. You’re only ever measuring an instant in time. So for price to be a measure of opportunity cost, then as you go forward in time, you need to know how all the opportunity costs have changed along with the current price of whatever you’re measuring. To do this, you have to make an assumption that opportunity costs are not changing over time. Mises seems to touch on this point in Epistemological Problems in Economics: you have to define an ends to which the action is attempting to obtain. Unless you’re aware of what the actor perceives as the next best alternative at all points in time, you inherently have an incomplete data set.
It goes even further. Say you had a complete data set for an instant in time to where you could create a supply and demand curve. That supply and demand curve would only be valid for that particular instant in time and only for that particular actor. This is why I have a problem with aggregate supply and demand curves and price time series. They’re never really measuring what price is supposed to represent – the opportunity cost of the next best action.
Do any of you know of a short, concise piece arguing against statistics in econ? The big pieces by the likes of Hoppe and Mises (and Hollis) are good, but I want something I can slide into my paper (i.e. summarise and evaluate) without breaking the word limits or spending excessive amounts of time on it. I’ve printed out Taleb’s paper. Is it worth incorporating in an essay on the methodology of economics or are his concerns restricted to finance? Rothbard has some good concise pieces on the amenability of human action to mathematical treatment in footnotes in MES, but I am already aware of and will be using those. North’s (critical) paper on Rothbard’s use of graphs is good but too extensive since I’m already using other longer materials. Maybe by Hayek in his The Counter-revolution of Science? I have the book, and it seems to be a collection of many articles.
its not really addressing the applicability of statistics to understanding economic issues, but its an itneresting take from Rothbard.
Do you know where in EEPE he treats of it?
Thanks. I used the argument in one of my essays. I just wanted to know if there’s a source for it I could use, but it seems clear enough as you articulated it.